$\begingroup$Example: Both the 3rd stage and the service module of the Apollo/Saturn had restartable engines. For those engines, more that one start / shut down was part of the planned flight profile, so presumably they would also be shut down on fault conditions too, so I think the answer would be a confident "yes" (dependent upon engine design).$\endgroup$
– Anthony XAug 26 '13 at 0:16

$\begingroup$The thrust can be regulated through nozzle geometry - e.g. it can be made completely inefficient; same amount of fuel is burned, exhaust gas is ejected but the vectors are all off, the gas doesn't provide much significant propulsion. The fuel can be segmented, so that once a segment burns off another isn't ignited and the motor stops, then the next segment is ignited and the motor starts anew - so it can be extinguished and reignited but not at arbitrary point but in several seconds of sector burn time quanta. This can be done. Now is it done in space rockets? I don't know.$\endgroup$
– SF.Aug 26 '13 at 12:14

$\begingroup$@AnthonyX The Saturn engines of Apollo were shut down on detected fault conditions. See for example the pogo issues on Apollo 13.$\endgroup$
– a CVnOct 6 '15 at 20:17

When
thrust is desired, a suitable
ignition source is introduced in
the combustion chamber and
the valve is opened. The liquid
propellant (or gas) flows into
the combustion chamber where
it is vaporized and then
reacted with the solid
propellant. Combustion occurs
in a boundary layer diffusion
flame adjacent to the surface
of the solid propellant.

so in hybrid rocket burning can be controlled by controlling the valve (or) by controlling the nozzle geometry

$\begingroup$Some solid fuel rockets may be shut down by blowing a big hole into the hull. Some solid propellants need a minimum pressure to continue burning, if the pressure is to low the propellant stops burning.$\endgroup$
– UweAug 1 '18 at 10:48

$\begingroup$@Uwe what did you mean here by "blowing a big hole into the hull", is there a fail-safe that uses this methodology? Like a giant hole-punch...?$\endgroup$
– Magic Octopus UrnAug 21 '18 at 21:09

2

$\begingroup$@MagicOctopusUrn Blow-out panels in the side of the motor. They're most often used with ICBMs to shut down the thrust when the desired trajectory has been reached. I'm not sure if any orbital launchers have used the technique.$\endgroup$
– Russell BorogoveApr 3 at 15:26

Liquid fueled

Most (almost all, but not all) are configured for both shut-off and restart.

Some early liquid fueled rockets could not be shut off - they were "gravity fed," and once under acceleration, could not be shut off, as the acceleration itself drove the fuel into the ongoing combustion.

Likewise, some military tactical rockets are non-stoppable liquid fuel rockets.

Solid Fueled

Most solid fuel rockets are not stoppable. This is due to the fuel mass usually being both fuel and oxidizer mixed in a stable but ignitable configuration.

A few theoretical designs use a solid oxidizer mass adjacent to a solid fuel mass, and one or the other can be ejected.

A few theoretical designs use multiple linear cells, and can have the currently burning cell ejected by a mechanical or pyrotechnic method; in theory later cells could have igniters. I've only seen this used in model rocketry; it's theoretically possible to cap an ejection charge such that it ejects motor 1 without igniting motor 2, and then have, past the cap, a remote ignition for motor 2 that, when it fires, ejects the cap. (I saw someone try to launch just such a rig; I didn't see it fly, due to engine 1 failure.)

Hybrid Motors

In hybrid motors, the fuel is usually solid, and the oxidizer is liquid. The motor is able to be shut off by stopping the oxidizer flow.

Some such motors use a hypergolic pair - that is, a pair that ignites on contact. Such motors are almost always able to be restarted.

Other motors include a re-ignition system of some kind, so that they can be restarted.

Abort Methods

Solid Rocket Boosters have often been configured such that they can be detached after ignition but before launch; generally, this is similar to a normal separation event. While this does not turn off the engine, it does allow the engine to launch without the rest of the craft, and from a payload perspective, is preferential to losing the payload as well.

Most NASA, ESA, and Russian Space Agency space launches also have charges to destroy the launch vehicle; manned launches also have an escape rocket that pulls the manned portion away prior to the rocket's destruction sequence. Again, this is not ideal, and isn't really a safe shutdown, but is used to protect downrange ground items from a failed launch.

With liquid fuel and hybrid fuel rockets, the first step of abort is to cease fuel flow; if that fails, then the payload eject and detonate protocols are invoked. With mixed launchers, both SRB detach and then escape/eject and if needed, destruction of the launcher are public listed protocols.

More advanced solid rocket motors can not only be throttled but also be extinguished
and then re-ignited by controlling the nozzle geometry or through the use of vent
ports. Also, pulsed rocket motors that burn in segments and that can be ignited upon
command are available.

Qualifier:

The page says rockets, not necessarily rockets meant for space-craft (either launch, or for use in space)

$\begingroup$If the solid rocket is extinguished by the use of vent ports, these ports must be closed and sealed before another ignition is possible. But you can't use rubber seals for that purpose. Another ignition requires a second starting charge inside the rocket, but this charge should not be damaged or even burnt during the first burn. The second starting charge must be shielded during the first burn, but the shield should be removed before the second ignition.$\endgroup$
– UweNov 15 '16 at 16:03

Modern solid fueled missile systems use so called "blow off ports" near the top of the motor in order to decrease the pressure of the combustion chamber and effectively "shut down" the thrust generation.

The burning rate of a solid propellant is dictated by: rate = a*P**n

So if the P (chamber pressure) could be brought to a near vacuum, the burning rate will decrease to near 0.

$\begingroup$That might reduce the thrust, but it does not stop it completely, and it certainly does not stop the propellant from being used up. There would not be any propellant left to restart later. I don't think this counts as "shutting off" the engine.$\endgroup$
– uhohJan 2 '18 at 14:50

2

$\begingroup$However, according to this answer there might be a way. In that case, your answer would just be stating what's already said in that answer.$\endgroup$
– uhohJan 2 '18 at 14:52